Question: Which of the following numbers is a factor of 171? ${3,6,7,8,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $171$ by each of our answer choices. $171 \div 3 = 57$ $171 \div 6 = 28\text{ R }3$ $171 \div 7 = 24\text{ R }3$ $171 \div 8 = 21\text{ R }3$ $171 \div 14 = 12\text{ R }3$ The only answer choice that divides into $171$ with no remainder is $3$ $ 57$ $3$ $171$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $3$ are contained within the prime factors of $171$ $171 = 3\times3\times19 3 = 3$ Therefore the only factor of $171$ out of our choices is $3$. We can say that $171$ is divisible by $3$.